I had to do the Myers-Briggs Type Indicator when I worked for the Federal government. It wasn't part of hiring, but after onboarding.

Best part of that? The group sessions that involved demonstrated examples of how different types interact or see things... I was basically called out as the anomaly (I'm an INTJ--NT being a largely male type), and asked how I liked being seen as a b*tch. fun times.

When my husband worked for one of the Bell companies, they started having a hiring personality screen. New hires had to meet a 'standard' set by HR types. Hubby is a computer programmer. They had to petition HR to change the standards for tech types because they couldn't find anyone who fit the standard and was qualified for the job.